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The primary reasoning I've heard is that it's easier to do arithmetic with numbers that are factors of your numeral base and 12 has more factors than 10 (1, 2, 3, 4, 6, 12 vs. 1, 2, 5, 10)
Base 12 seems a little impractical to me since humans have 10 fingers, which makes base 10 easier to teach to children, but it's a matter of opinion i guess
τ is equal to 2π, which allows the formula for the circumference of a circle to be written more concisely (τr vs. 2πr or πd) but complicates most other places where π is used, like in the area of a circle (τr^2/2 vs. πr^2)
My response to the 10 fingers thing is that it's easier to do certain calculations in your head. A lot of those calculations are larger than 10, anyway, so your fingers don't help.
A third of 24 is 8. A third of 60 is 20. It becomes second nature after a while.
One place I used this a lot was 40k. In between rolls, I grouped my dice into sets of 4. When the next roll called for 12 dice, I quickly pick up 3 sets. If it's 10, pick up two sets plus two dice from a third set. Made it really quick to count. At least for the base rolls, a lot of the stats in 40k tend to work in multiples of 4, so this worked out.